We study the environment under two different matching mechanisms.
The first is the well-known student-optimal deferred acceptanceThis is a variant of the Gale-Shapley matching mechanism. (DA) mechanism [1]}. The mechanism works as follows. First, the students apply to their most preferred school. The schools reject the lowest ranking students who exceed their capacity limit. Not rejected students are held temporarily. If a student is rejected, she applies to the next school in the preference order. The schools take temporarily admitted and newly applying students into account and reject the lowest ranking students that exceed the capacity. This process repeats until no more students apply or are rejected. The DA mechanism is strategy-proof, i.e., truth-telling is a dominant strategy.
